scholarly journals What can the observation of nonzero curvature tell us?

2012 ◽  
Vol 86 (2) ◽  
Author(s):  
Alan H. Guth ◽  
Yasunori Nomura
Keyword(s):  
Nonzero Curvature

scholarly journals NAMBU–JONA–LASINIO MODEL IN CURVED SPACETIME WITH MAGNETIC FIELD

1996 ◽  
Vol 11 (25) ◽  
pp. 2053-2063 ◽  
Author(s):  
B. GEYER ◽  
L.N. GRANDA ◽  
S.D. ODINTSOV
Keyword(s):  
Magnetic Field ◽  
Gravitational Field ◽  
Chiral Symmetry ◽  
Proper Time ◽  
Chiral Symmetry Breaking ◽  
Curved Spacetime ◽  
Njl Model ◽  
Nonzero Curvature ◽  
Curvature Approximation ◽  
The Magnetic Field

We discuss the phase structure of the NJL model in curved spacetime with magnetic field using 1/N-expansion and linear curvature approximation. The effective potential for composite fields [Formula: see text] is calculated using the proper-time cutoff in the following cases: (a) at nonzero curvature, (b) at nonzero curvature and nonzero magnetic field, and (c) at nonzero curvature and nonzero covariantly constant gauge field. Chiral symmetry breaking is studied numerically. We show that the gravitational field may compensate the effect of the magnetic field what leads to restoration of chiral symmetry.

scholarly journals On hypersurfaces in a locally affine Riemannian Banach manifold

2002 ◽  
Vol 31 (6) ◽  
pp. 375-379
Author(s):  
El-Said R. Lashin ◽  
Tarek F. Mersal
Keyword(s):  
Riemannian Manifold ◽  
Second Order ◽  
Banach Manifold ◽  
Infinite Dimensional ◽  
Nonzero Curvature

We prove that an essential hypersurface of second order in an infinite dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature.

scholarly journals On hypersurfaces in a locally affine Riemannian Banach manifold II

2004 ◽  
Vol 2004 (2) ◽  
pp. 99-104
Author(s):  
El-Said R. Lashin ◽  
Tarek F. Mersal
Keyword(s):  
Banach Space ◽  
Riemannian Manifold ◽  
Second Order ◽  
Banach Manifold ◽  
Riemannian Curvature ◽  
Infinite Dimensional ◽  
Nonzero Curvature

In our previous work (2002), we proved that an essential second-order hypersurface in an infinite-dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature. In this note, we prove the converse, in other words, we prove that a hypersurface of constant nonzero Riemannian curvature in a locally affine (flat) semi-Riemannian Banach space is an essential hypersurface of second order.

A Uniform L∞ Estimate of the Smoothing Operators Related to Plane Curves

1997 ◽  
Vol 40 (4) ◽  
pp. 433-442
Author(s):  
Kanghui Guo
Keyword(s):  
Spectral Synthesis ◽  
Plane Curve ◽  
Plane Curves ◽  
Zero Curvature ◽  
Nonzero Curvature

AbstractIn dealing with the spectral synthesis property for a plane curve with nonzero curvature, a key step is to have a uniform L∞ estimate for some smoothing operators related to the curve. In this paper, we will show that the same L∞ estimate holds true for a plane curve that may have zero curvature.

Reverse time migration of multiples: Eliminating migration artifacts in angle domain common image gathers

Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. S263-S270 ◽  
Author(s):  
Yibo Wang ◽  
Yikang Zheng ◽  
Lele Zhang ◽  
Xu Chang ◽  
Zhenxing Yao
Keyword(s):  
Free Surface ◽  
Radon Transform ◽  
Synthetic Data ◽  
Velocity Model ◽  
Migration Velocity ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Time Migration ◽  
Nonzero Curvature

Free-surface-related multiples are usually regarded as noise in conventional seismic processing. However, they can provide extra illumination of the subsurface and thus have been used in migration procedures, e.g., in one- and two-way wave-equation migrations. The disadvantage of the migration of multiples is the migration artifacts generated by the crosscorrelation of different seismic events, e.g., primaries and second-order free-surface-related multiples, so the effective elimination of migration artifacts is crucial for migration of multiples. The angle domain common image gather (ADCIG) is a suitable domain for testing the correctness of a migration velocity model. When the migration velocity model is correct, all the events in ADCIGs should be flat, and this provides a criterion for removing the migration artifacts. Our approach first obtains ADCIGs during reverse time migration and then applies a high-resolution parabolic Radon transform to all ADCIGs. By doing so, most migration artifacts will reside in the nonzero curvature regions in the Radon domain, and then a muting procedure can be implemented to remove the data components outside the vicinity of zero curvature. After the application of an adjoint Radon transform, the filtered ADCIGs are obtained and the final denoised migration result is generated by stacking all filtered ADCIGs. A three-flat-layer velocity model and the Marmousi synthetic data set are used for numerical experiments. The numerical results revealed that the proposed approach can eliminate most artifacts generated by migration of multiples when the migration velocity model is correct.

scholarly journals f(R) TERM AND GEOMETRIC ORIGIN OF THE DARK SECTOR IN HOŘAVA–LIFSHITZ GRAVITY

2011 ◽  
Vol 26 (06) ◽  
pp. 387-398 ◽  
Author(s):  
ANZHONG WANG
Keyword(s):  
Detailed Balance ◽  
De Sitter ◽  
Dark Sector ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Nonzero Curvature ◽  
Geometric Origin ◽  
The Universe ◽  
Scalar Perturbations ◽  
Scalar Mode

Inclusion of f(R) term in the action of Hořava–Lifshitz quantum gravity with projectability but without detailed balance condition is investigated, where R denotes the 3-spatial dimensional Ricci scalar. Conditions for the spin-0 graviton to be free of ghosts and instability are studied. The requirement that the theory reduces to general relativity in the IR makes the scalar mode unstable in the Minkowski background but stable in the de Sitter. It is remarkable that the dark sector, dark matter and dark energy, of the universe has a naturally geometric origin in such a setup. Bouncing universes can also be constructed. Scalar perturbations in the FRW backgrounds with nonzero curvature are also studied.

scholarly journals Characterization of Rectifying and Sphere Curves in ℝ3

2017 ◽  
Vol 14 (2) ◽  
Author(s):  
Julie Logan ◽  
Yun Myung Oh
Keyword(s):  
Tangent Vector ◽  
Normal Vector ◽  
Extra Condition ◽  
Space Curves ◽  
3D Space ◽  
Nonzero Curvature ◽  
Unit Speed ◽  
Curvature And Torsion ◽  
Rectifying Curve

Studies of curves in 3D-space have been developed by many geometers and it is known that any regular curve in 3D space is completely determined by its curvature and torsion, up to position. Many results have been found to characterize various types of space curves in terms of conditions on the ratio of torsion to curvature. Under an extra condition on the constant curvature, Y. L. Seo and Y. M. Oh found the series solution when the ratio of torsion to curvature is a linear function. Furthermore, this solution is known to be a rectifying curve by B. Y. Chen’s work. This project, uses a different approach to characterize these rectifying curves. This paper investigates two problems. The first problem relates to figuring out what we can say about a unit speed curve with nonzero curvature if every rectifying plane of the curve passes through a fixed point in ℝ3. Secondly, some formulas of curvature and torsion for sphere curves are identified. KEYWORDS: Space Curve; Rectifying Curve; Curvature; Torsion; Rectifying Plane; Tangent Vector; Normal Vector; Binormal Vector

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